Circular waveguide diameter transformer



Jan. 30, 1962 D. A. LANCIANI ETAL CIRCULAR WAVEGUIDE DIAMETERTRANSFORMER Filed March 6, 1959 2 F|G.l

FIG.2

. JNVENTORS DANIEL A. LANCIANI ARTHUR A. BLAISDE'LL ATTORNEY Uite Statesatent 3,019,399 Patented Jan, 30, 1962 fire 3,019,399 CIRCULAR WAVEGUIDEDIAMETER TRANSFORMER Daniel A. Lanciani, West Medford, and Arthur A.Biaisdell, Naticir, Mass., assignors to Microwave Associates,

Inc., Burlington, Mass., a corporation of Massachusetts Filed Mar. 6,195), Ser. No. 797,667 11 Claims. (Cl. 33334) This invention relates tothe propagation of electromagnetic wave energy in circularly symmetricalmodes in round hollow pipe waveguide, and more particularly totransformers from small to large waveguide and vice versa for acircularly symmetrical wave.

In the propagation of electromagnetic wave energy in round hollow pipewaveguides it is well known that the energy can propagate in one or moremodes, or characteristic field configurations, depending on thecross-sectional size, or internal diameter, of the particular waveguide,and on the operating frequency, and that the larger the internaldiameter is made the greater is the number of modes in which the energycan propagate at a given operating frequency. It is usually desirable toconfine propagation of the energy to one particular mode, depending uponthe application which is involved. If the desired mode is also theso-called dominant mode, the diameter of the waveguide can be restrictedso that no other modes can be propagated in it. The TE mode, inconnection with which the present invention is described, is frequentlychosen for its ability to propagate over long waveguide distances withless attenuation than other modes. It is, however, not the dominantmode, and the diameter of a waveguide in which this mode will propagatemust be so large that other modes can also be propagated in itthat is,the waveguide is a multimode circular waveguide.

In certain instances it is desirable to effect a change in the diameterof a multimode circular waveguide intended for propagation of a givenmode, such as the TE mode. For example, it is desirable to do this totransform the impedance of the waveguide from one value to another. Whena change in the diameter is effected, it is also desirable to do so witha minimum of mode conversion.

A commonly used technique to solve this problem is to resort to the useof a conical tapered section of waveguide between the two sections ofsmaller and larger diameter waveguide. Since the effective modeconversion is an inverse function of the length of the tapered section,mode conversion can be minimized by the use of a long tapered section.This usually results in a structure which is longer than is desirable ortolerable for many applications.

Another technique has been described by S. P. Morgan, Jr., in U.S.Patent No. 2,762,982, which uses dielectric mode converters toeffectively cancel spurious modes which have been generated in passingfrom a smallerdiameter waveguide to a larger-diameter waveguide througha tapered section. This method, too, since it involves the use of atapered section of waveguide in addition to the dielectric modeconverters, usually results in a structure which is undesirably orintolerably long for many applications.

It is an object of the present invention to provide a diametertransformer for round hollow pipe waveguides which is of greatly reducedlength compared to a tapered pipe section or to devices involvingdielectric mode converters, and which preserves the mode purity ofelectromagnetic waves propagating in it with an efficiency as good asthat of a tapered section of much greater length. Other objects are toprovide such a transformer of simple design, which is not expensive orcomplex to fabricate. or difficult to use and which is inherently ofrugged and durable construction.

According to the invention, these objects are attained by providing atransformer in which the internal diameter is increased in a series ofsteps. In multimode circular waveguide an abrupt diametral change willcause mode conversion to occur; that is, a transfer of a portion ofenergy propagating in the desired mode to other modes of propagationtakes place. The step transformer of the present invention makes use ofthe mode generation properties of a diametral step and of theprogressive phase shift of the generated mode or modes to reduce the netmode conversion to zero or a negligible value in a relatively shortlength of transmission line. Thus, for example, with essentially pure TEmode energy propagating in a round hollow waveguide, the diameter isincreased in steps, which are circularly symmetrical, and of such smallsize that substantially the only impurity excited by each step is the TEmode. The steps are arranged to excite controlled magnitudes, forexample, equal magnitudes of energy in the TE mode, and areappropriately phased to produce an effective cancelling of the TEimpurity.

In one practical embodiment, transformation from small to oversize (forthe TE mode) circular waveguide is achieved by the use of a series ofquarter wavelength (i.e., guide wavelength) steps in the TE mode up tothe maximum critical diameter which is below cut-off for the TE mode.From this point, the step discontinuities are made as small as practicalbut equal in regard to TE mode excitation. Then by proper spacing of thesteps the phase relations of the TE waves which are excited are adjustedfor effective cancellation.

Other and further objects and features of the inventionare set forth inthe detailed description of certain embodiments thereof which follows.The description refers to the accompanying drawings, wherein:

FIG. 1 illustrates in side section a step transformer made of a singlepiece of solid material; and

FIG. 2 illustrates in side section a step transformer con-.

structed of telescoping sections of separate tubing.

In FIG. 1, the transformer according to the invention is comprised of aseries of circular bores of progressively increasing internal diametersD D D D D and D respectively, in a single piece of metal 10. Each ofthese bores constitutes a section of circular wave-guide of uniformdiameter, and the series of waveguide sections constitutes in effect asingle circular waveguide of which the internal diameter progressivelyincreases in discrete steps from the smallest diameter D, to the largestdiameter D The smallest diameter D and the next three langer diameters DD and D,, are all below cutoff for the TE mode at the operatingfrequency, the' largest of these diameters D being the maximum criticaldiameter which is below cut-off for that mode. The wave-- adjacentdiameters, that is, the ratios D /D D /D and D1 2/D are related to eachother according to a binomial distribution, as well be more fullyexplained below.

The next larger diameter D is able to support the T13 mode at theoperating frequency. The step from diameter D to diameter D is madesufficiently small so that when pure TE mode energy enters the largerguide section substantially the only impurity excited by thediscontinuity is the T13 mode. Ability to achieve this result isenhanced by the fact that the discontinuity has circular symmetry. Aconsideration which restricts to some degree the minimum step size thatcan be used is the need to make the first step beyond the maximumcritical diameter D sufiiciently 'large to permit propagation of the TEmode at the lowest frequency in the operating band. The succeeding stepfrom diameter D to diameter D, is chosen to excite TE energy, from theTE energy incident upon it, equal in magnitude to the TE energy excitedby the step from diameter D to diameter D These two steps, from D to Dand from D to D are spaced with respect to the guide wavelength for theTE mode so that these equal magnitudes of step-excited T5 mode energyare in phase opposition-i.e., they differ in phase by 180". Thisproduces effective cancellation of the TE impurity.

The design considerations for the step sizes and spacings in thesections of diameters D D and D are as follows. If a pure TE mode waveis incident at the plane A between the two guide sections of diameters Dand D the energy content of the Wave is divided into two componentmodes, 13 and E where E E When the E component reaches the plane Bbetween the two guide sections of diameters D and D its energy contentwill again divide into two component modes, E' and E' The total T15 modecomponent at plane B is, therefore, E0g +E 02 In order for thissummation to be equal to zero, the following two conditions must besatisfied:

|E |=]E (Condition 1) and where N=any odd integer (Condition 2)Condition 1 is approximately satisfied if D /D =D /D Condition 2 issatisfied if the distance L between the planes A and B has a magnitudecomputed from the following relation:

Where N=any odder integer. (Relation 1) In Relation l, the expression kflD means the guide Wavelength for the TE mode in the section ofdiameter D and the expression A (D means the guide wavelength for the TEmode in the same section.

In the guide sections of internal diameters D D D and D which are allbelow cut-off for the TE mode, it is only necessary to space the stepsgtll 4 apart. In the present embodiment, which employs three steps to gofrom the smallest diameter D to the maximum critical diameter D the stepsizes are binomia-lly related, so that the TE mode disturbance createdat the intermediate plane X will be twice the magnitude of the T E modedisturbance created at each of the outer planes Y and Z; the latterdisturbances are of equal magnitude. The larger TE mode disturbance isthen cancelled half by the TE mode disturbance created at plane Y andhalf by the TE mode disturbance created at plane Z.

An impedance transformer designed for use with a TE mode circularwaveguide of internal diameter 0.634 inch intended for operation at afrequency of approximately 35,000 mc./sec., has been built with thefollowing dimensions (referring to FIG. 1):

D =0.634 inch inch inch D =0f700 inch D =0.835 inch D =0.995 inch L=0.382 inch L =0.694 inch L =0.80 1 inc-h L.;=0.9l1 inch From thesedimensions, the step ratios of the guide sections of critical diameter(D and less are:

which are practically identical.

Tests of mode conversion from TE to TE in the output of two transformersconstructed according to FIG. 1 with the foregoing dimensions, employinga signal centered at 34,860 mc./sec. (i.e., 34.86 kmc./s.), yielded thefollowing results:

Mode (TE to Frequency Conversion, TE

Sample Sample No. 1 No. 2

Percent Percent 34.85 kmo/s O. 3 0. 4 34.00 kinC./s 1. 8 2. 4 36.00kmcJs 0 5 0.5

These results are substantially identical with those which can beachieved using a tapered round hollow waveguide one foot long to gouniformly from D to D They are attained with step transformers accordingto the present invention which are less than one inch long (L =0.9llinch).

FIG. 2 illustrates a construction or" a step transformer according tothe invention utilizing a series of telescoping sections of circularwaveguide. A first section 21 of relatively the smallest inner diameterfits telescopically into a second section 22, which fits telescopicallyinto a third section 23, and so forth to sections 24, 25 and 26. Thewall thicknesses of the various sections are chosen to provide thedesired step sizes, for example according to the design considerationsdescribed above with reference to FIG. 1, and the desired axial lengthsof the effective waveguide sections of the various inner diameters areachieved by relative telescopic adjustment of contiguous pairs of theoriginal waveguide sections. In a step transformer constructed in thismanner which changed from an inner diameter of 0.634 inch of the firstsection 21 to an inner diameter of 0.995 inch of the last section 26, insix steps, the result achieved was mode conversion to TE in the output,from essentially pure TE mode energy introduced via the first section21, on the order of two. to three percent. The size of each step in thistransformer was arbitrary, however, being governed by the wallthicknesses of available commercial tubing. Employing tubing fabricatedwith wall thicknesses chosen according to the design considerationsdescribed above, results similar to those set forth above can beachieved. This latter consideration, however, introduces the need for afabrication step, namely that of drawing or machining the individualtubing sections to desired sizes, unless available tubing can be foundwhich satisfies all the desired design parameters. In addition, theconcentricity of eachsection is critical, if circular symmetry of allthe steps is to be preserved. For these reasons, embodiments accordingto FIG. 1 are the preferred embodiments of the invention.

It will be recognized that embodiments of the invention can beconstructed having three or more steps in the sections of diameter abovecut-oif for the T13 mode. In such cases it may be advantageous to choosestep ratios which provide a step-generated TE mode amplitudedistribution which is other than equal for all the steps. For example, abinomial step distribution can be used. In the case of three steps, thestep-generated T15 mode amplitudes would desirably be distributed withthe relative values 121, as described above with reference to the threesteps in the region of diameters which are below the critical diameterfor the TE mode. In the case of four steps, the step-generated TE modeamplitudes would desirably be distributed with the relative values1-3-34, and for five steps a desirable relative amplitude distributionwould be 1464-l. Alternatively, a T chebyscheff step distribution may beemployed. In any case, it is preferred that the diameters of thewaveguide sections which will support the TE mode (D and D in FIG. 1,for example) be below cut-off for the TE mode.

The foregoing principles are valid also for transitions from diameterswhich are below cut-off for the TE mode to diameters above suchcut-oifi.e., for transformers from T15 to TE Q mode sized waveguide, andin general for designing step transformers from TE to TE +1) mode sizes.More generally, these principles are valid for diametric transformationfrom a size limited to any mode having circular symmetry to a size ableto propagate the next higher order of the same mode, or vice versa.

The embodiments of the invention which have been illustrated anddescribed herein are but a few illustrations of the invention. Otherembodiments and modifications will occur to those skilled in the art. Noattempt has been made to illustrate all possible embodiments of theinvention, but rather only to illustrate its principles and the bestmanner presently known to practice it. Therefore, while certain specificembodiments have been described as illustrative of the invention, suchother forms as would occur to one skilled in this art on a reading ofthe foregoing specification are also Within the spirit and scope of theinvention, and it is intended that this invention include allmodifications and equivalents which fall within the scope of theappended claims.

What is claimed is:

1. Diameter transformer for circular waveguide intended for propagationof electromagnetic wave energy in a prescribed first mode havingcircular symmetry to one or more larger diameters capable of propagatingenergy in a second mode which is the next higher order of said firstmode, comprising a circular waveguide the diameter of which, in a givenaxial direction, progressively increases stepwise at each of a pluralityof axially-spaced transverse planes, each section of said waveguidebetween adjacent pairs of said planes being of substantially constantdiameter, the diametral changes each being dimensioned to generate aprescribed amount of said second mode energy from the first mode energyat the operating frequency propagating through it, the magnitude of eachdiametral change being restricted so that substantially no energy in amode higher than said second mode is generated from said first modeenergy, the planes defining said diametral changes being spaced apartrelative to said second mode energy at the operating frequency so thatsaid amounts of second mode energy generated by the diametral change ateach of said planes due to incidence thereat of first mode energypropagating through said waveguide in a given direction substantiallycancel each other.

2. Diameter transformer for circular waveguide intended for propagationof electromagnetic wave energy in the TE mode, where n is an integer, toone or more larger diameters capable of propagating energy in the T Emode, comprising a circular waveguide the diameter of which, in a givenaxial direction, progressively increases stepwise at each of a pluralityof axially-spaced transverse planes, each section of said waveguidebetween adjacent pairs of said planes being of substantially constantdiameter, the diametral changes each being dimensioned to generate aprescribed amount of TE mode energy from TE mode energy at the operatingfrequency propagating through it, the magnitude of each diametral changebeing restricted so that substantially no energy in a mode higher thansaid TE mode is generated from said TE mode energy, the planes definingsaid diametral changes being spaced apart relative to TE mode energy atthe operating frequency so that said amounts of TE mode energy generatedby the diametral change at each of said planes due to incidence thereatof TE mode energy propagating through said waveguide in a givendirection substantially cancel each other.

3. Diameter transformer for circular waveguide intended for propagationof electromagnetic wave energy in the TE mode comprising a circularwaveguide the diameter of which progressively increases stepwise at eachof a plurality of consecutive axially-spaced transverse planes, eachsection of said waveguide between adjacent pairs of said planes being ofsubstantially constant diameter, the diametral changes each beingdimensioned to generate a prescribed amount of "SE mode energy from TEmode energy at the operating frequency propagating through it, themagnitude of each diametral change being restricted so thatsubstantially no energy in a mode higher than said TE mode is generatedfrom said TE mode energy, the planes defining said diametral changesbeing spaced apart relative to TE mode energy at the operating frequencyso that said amounts of TE mode energy generated by the diametral changeat each of said planes due to TE mode energy propagating through saidwaveguide in a given direction substantially cancel each other.

4. Diameter transformer for circular waveguide intended for propagationof electromagnetic wave energy in the TE mode comprising a circularwaveguide the diarneter of which progressively increases stepwise ateach of a plurality of consecutive aXiallly-spaced transverse planes,each section of said waveguide between adjacent pairs of said planesbeing of substantially constant diameter, one of said diametralincreases being from a section of diameter below cut-off for the TE modeat the operating frequency to a section above cut-off for said mode,said one diametral increase being followed by at least one furtherdiametral increase, said one and said following diametral increases eachbeing dimensioned to generate a prescribed amount of TE mode energy fromTE mode energy at the operating frequency propagating through it, themagnitude of each of said one and said following diametral increasesbeing restricted so that substantially no energy in a mode higher thansaid TE mode is generated from said TE mode energy, the planes definingsaid one and said following diametral increases being spaced apartrelative to TE mode energy at the operating frequency so that saidamounts of TE mode energy generated by the diametral change at each ofsaid planes due to inci dence thereat of TE mode energy propagatingthrough said waveguide in a given direction substantially cancel eachother.

5. Diameter transformer for circular waveguide intended for propagationof electromagnetic wave energy in the TE mode comprising a circularwaveguide the diameter of which progressively increases stepwise at eachof a plurality of consecutive axially-spaced transverse planes, eachsection of said waveguide between adjacent pairs of said planes being ofsubstantially constant diameter, the first diametral increase being froma section of the maximum critical diameter which is below cut-off forthe TE mode at the operating frequency to a section above cut-off forsaid mode, the diametral increases each being dimensioned to generate aprescribed amount of TE mode energy from TE mode energy at the operatingfrequency propagating through it, the magnitude of each diametralincrease being restricted so that substantially no energy in a modehigher than said TE mode is generated from said TE mode energy, saidplanes being spaced apart relative to TE mode energy at the operatingfrequency in the sections between them so that said amounts of TE modeenergy generated by the diametral change at each of said planes due toincidence thereat of TE mode energy propagating through said Waveguidein a given direction substantially cancel each other.

6. Diameter transformer for circular waveguide intended for propagationof electromagnetic wave energy in the TE mode comprising a circularwaveguide the diameter of which progressively increases stepwise at eachof two consecutive axially-spaced transverse planes, each section ofsaid waveguide between adjacent pairs of said planes being ofsubstantially constant diameter, the first diametral increase being froma section of diameter below cut-off for the TE mode at the operatingfrequency to a section above cut-off for said mode, the diametralincreases each being dimensioned to generate substantially equal amountsof TE mode energy from TE mode energy at the operating frequencypropagating through them in the direction of increasing diameters, themagnitude of each diametral increase being restricted so thatsubstantially no energy in a mode higher than said T13 mode is generatedfrom said TE mode energy, said planes being axially spaced apartrelative to T E mode energy at the operating frequency in the waveguidesection between them so that said amounts of TE mode energy generated ateach of said planes due to incidence thereat of TE mode energypropagating through said waveguide in said direction substantiallycancel each other at the increase to the largest diameter.

7. Internal diameter transformer for hollow round waveguide intended forpropagation of electromagnetic wave energy in the TE mode comprising around hollow waveguide the internal diameter of which progressivelyincreases stepwise at each of a plurality of consecutive axially-spacedtransverse planes, each section of said waveguide between adjacent pairsof said planes being of substantially constant diameter, one of saiddiametral increases being from a section of internal diameter belowcut-01f for the T E mode at the operating frequency to a section abovecut-oil? for said mode, said one diametral increase being followed by atleast one further internal diametral increase, said one and saidfollowing internal diametral increases each being dimensioned togenerate a prescribed amount of T13 mode energy from T13 mode energy atthe operating frequency propagating through it, the magnitude of each ofsaid one and said following diametral increases being restricted so thatsubstantially no energy in a mode higher than said TE mode is generatedfrom said TE mode energy, the planes defining said one and saidfollowing diametral increases being spaced apart elative to TE modeenergy at the operating frequency so that said amounts of TE mode energygenerated by the diametral change at each of said planes due toincidence thereat of TE mode energy propagating through said waveguidein a given direction substantially cancel each other.

8. Internal diameter transformer for hollow round waveguide intended forpropagation of electromagnetic wave energy in the TE mode comprising around hollow waveguide made of a single piece of electrically conductivematerial the internal diameter of which progressively increases stepwiseat each of a plurality of consecutive axially-spaced transverse planes,each section of said waveguide between adjacent pairs of said planesbeing of substanitally constant diameter, one of said diarnetralincreases being from a section of internal diameter below cut-off forthe TE mode at the operating frequency to a section above cut-off forsaid mode, said one diametral increase being followed by at least onefurther internal diametral increase, said one and said followinginternal diametral increases each being dimensioned to generate aprescribed amount of TE mode energy from TE mode energy at the operatingfrequency propagating through it, the magnitude of each of said one andsaid following diametral increases being restricted so thatsubstantially no energy in a mode higher than said TE mode is generatedfrom said T5 mode energy, the planes defining said one and saidfollowing diametral increases being spaced apart relative to TE modeenergy at the operating frequency so that said amounts or" TE modeenergy generated by the diametral change at each of said planes due toincidence thereat of TE mode energy propagating through said waveguidein a given direction substantially cancel each other.

9. Internal diameter transformer for hollow round waveguide intended forpropagation of electromagnetic wave energy in the TE mode comprising around hollow waveguide the internal diameter of which progressivelyincreases stepwise at each of a plurality of consecutive axially-spacedtransverse planes, each section of said waveguide between adjacent pairsof said planes being of substantially constant diameter, the firstdiametral increase being from a section of internal diameter belowcut-01f for the TE mode at the operating frequency to a section abovecut-off for said mode, the diametral increases each being dimensioned togenerate a prescribed amount of TE mode energy from T E mode energy atthe operating frequency propagating through it, the magnitude of eachdiametral increase being restricted so that substantially no energy in amode higher than said TE mode is generated from said TE mode energy,said planes being spaced apart relative to TE mode energy at theoperating frequency in the sections between them so that said amounts ofTE mode energy generated by the diametral change at each of said planesdue to incidence thereat of TE mode energy propagating through saidwaveguide in a given direction substantially cancel each other.

10. Internal diameter transformer for hollow round waveguide intendedfor propagation of electromagnetic wave energy in the TE- modecomprising, a first section of round hollow waveguide having a firstsubstantially constant internal diameter which is below cut-off for theTE mode at the operating frequency, a second section of round hollowwaveguide having a second substantially constant internal diameter whichis greater than said first internal diameter and is above cut-off forthe TE mode at the operating frequency, said first and second sectionsmeeting concentrically at a first plane transverse to their common axisto provide in said first plane a first circularly symmetrical stepwisediametral change, a third section of round hollow waveguide having athird substantially constant internal diameter which is greater thansaid second internal diameter, said second and third sections meetingconcentrically at a second plane transverse to their common axis toprovide in said second plane a second circularly symmetrical stepwisediametral change, the length of said second section between said firstand second planes being determined by the relation where:

N=any odd integer,

and said diameters being so related that D ==said first diameter,

D =said second diameter, and

D =said third diameter, the magnitude of each diametral change from D toD and from D to D respectively, being restricted so that substantiallyno energy in a mode higher than said TE mode is generated from said 'I'Emode energy passing therethrough.

an internal diameter which is above cut-off for said mode,

said last named section being followed by at least one more section ofstill larger internal diameter, the diametral increases to internaldiameters which are above cutoff for said TE mode each being dimensionedto generate a prescribed amount of TE mode energy from TE mode energy atthe operating frequency propagating through it in the direction ofincreasing internal diameters, the magnitude of each diametral increasebeing re stricted so that substantially no energy in a mode higher thansaid TE mode is generated from said T13 mode energy, the planes definingsaid last named diametral increases being spaced apart relative to TEmode energy at the operating frequency so that said amounts of TE modeenergy generated at each of said planes due to incidence thereat of TEmode energy propagating through said waveguide in said directionsubstantially cancel each other.

References Cited in the file of this patent UNITED STATES PATENTS2,531,437 Johnson et a1. Nov. 28, 1950 2,643,296 Hansen June 23, 19532,762,982 Morgan a- Sept. 11, 1956 2,767,380 Zobel Oct. 16, 1956 FOREIGNPATENTS 147,078 Australia Sept. 9, 1948 OTHER REFERENCES CollinProceedings of the IRE, Feb. 1955, vol. 43, No. 2, pages 179-185.

Olin Electronics, Dec. 1955, pages 146 and 147.

Unger: Bell System Tech. Journal, vol. 37, No. 4, July 1958, pages899-912.

Wray: Electronic Engineering, vol. 31, No. 372, Feb. 1959, pages 7679.

